Propagation Characteristics and Overvoltage Analysis on Unconventional Submarine Cables

Transcription

1 1 Propagation Characteristics and Overvoltage Analysis on Unconventional Submarine Cables Paulo E.D. Rocha, Antonio C. S. Lima, Sandoval Carneiro Jr. Abstract There are some submarine cables also known as umbilical cables which are finding a growing use in the oil industry. One of the advantages of such cables is that they can combine both structural and electrical cables thus providing a more compact installation. From the electrical point of view these cables can be seen as a pipe-type inside another pipe-type. The electrical parameters, namely the impedance and admittance per unit of length of such cables cannot be calculated using conventional cable parameters subroutine available in Electromagnetic Transient (EMT) Programs such as EMTP-RV, ATP. However the procedures used in those subroutines can be expanded for the analysis of the umbilical cases. This paper presents a review of the basic procedures commonly used for evaluation of the cables impedance and admittance per unit of length as well as outlines the changes needed in order to represent the umbilical. The cable parameters are used in a Frequency Domain program to assess an overvoltage analysis as well as an analysis of the propagation characteristics of the submarine cable system. Index Terms Frequency-Dependent Pipe-Type Models, Electromagnetic Transients I. Introduction Some industries, such as the oil companies are experiencing a large expansion and may need some unconventional power transmission networks. Furthermore, the environmental issues creates a great concern in the oil industries, so reliability is very important. Furthermore, electromagnetic transients studies are of paramount importance for the correct assessment of the Electrical Network performance and accurate models are needed to assure the accuracy of the simulations. In countries with deep oil wells the companies are using some unconventional cable that are considerably different from the ones usually found in underground power transmission. For instance, these unconventional cables may have several pipes with power conductors, cooling hoses, optical devices. The cost of an oil installation together with the need for reliability have placed a high demand on the accuracy of the electrical studies. This work was supported in part by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, CNPq, Brazil, PETROBRAS Research center, CENPES, Brazil, and Fundação de Amparo à Pesquisa Carlos Chagas, FAPERJ, Rio de Janeiro, RJ. P.E.D. Rocha, A.C.S. Lima and S. Carneiro Jr. are with Federal University of Rio de Janeiro, Department of Electrical Engineering, P.O. Box. 6854, , Rio de Janeiro, RJ, Brasil, ( acsl@dee.ufrj.br, sandoval@dee.ufrj.br) Presented at the International Conference on Power Systems Transients (IPST 7) in Lyon, France on June 4-7, 27 These unconventional cables also present a technological challenge as one may be involved with the calculation of the electrical parameters of a pipe inside another. Furthermore, the evaluation of pype-type cables alone is not straight forward as in single-core (SC) cables or overhead transmission lines. This is due to the fact that a pipe may contain SC cables which are not concentric. This work analyzes the propagation characteristics and the sheath, pipe overvoltages for this unconventional cable. The unconventional cable also known as umbilical cable is shown in Fig. 1. The detailed cable dimensions are shown in the appendix A. Umbilical cables can be understood as a pipe-type cable inside another pipe. Unfortunately, nowadays, this type of cable cannot be represented in EMTP type programs using the available Cable Constants (CC) routines. A stand alone program was build to calculate the cable parameters and the time domain responses were obtained using a Numerical Laplace Transform. Fig. 1. Umbilical cable II. Frequency Domain Analysis An umbilical cable as any transmission system can be represented by the characteristic admittance Y c and propagation function A, which are calculated from series impedance Z and shunt admittance Y, both per unit length, as follows: [ A = exp l ] Z(ω) Y (ω) Y c = Z 1 (1) Z(ω) Y (ω) where l is the length of the cable. As the umbilical cable is a system of n conductors, we have only n n matrices. The series impedance, per unit length, is given by: Z(ω) = Z int (ω) + Z pipe (ω) + Z ext (ω) (2)

2 2 where Z int (ω) = Z skin (ω)+z sol (ω)+z prox (ω) includes skin, solenoid and proximity effects; Z pipe (ω) = Z p (ω) + Z c (ω) represents the contribution of the first metallic layer of the surrounding pipe, as well as the coupling between the metallic layers in the pipe; Z ext = Z ideal (ω) + Z solo (ω) represents the mutual coupling between the conductors and external media. All the parameters in Z(ω) are frequency dependent. The shunt admittance per unit length Y = G + jωc, can be determined directly from Maxwell potential matrix. Usually the conductance G is neglected and Y = jωc. The capacitance C is frequency independent. In order to simplify the analysis, any saturation effect in the piper is neglected, and proximity and solenoid effects are neglected. As the main goal is the analysis of submarine cables, the external media is assumed homogeneous, linear, and unbounded with a relative magnetic permeability µ r = 1 constant throughout the whole frequency span considered for the analysis. All the losses in the dielectrics are neglected. The technical literature has already presented both accurate and approximate formulae for the evaluation of single-core cables [1]. For the analysis considered here two main structures are considered either considering more exact impedance expressions as well as approximate formulae as shown in Table I where the acronym reflects the different methodology to deal with the parameters. Therefore the configuration was compared against the results obtained using SASB using the data given by [2] [4]. Z c2 Z c4 Z c1 Z c2 Z c4 Z c (ω) = Z c2 Z c4 Z c2 Z c2 Z c2 Z c3 Z c4 Z c4 Z c4 Z c4 Z c4 Z c5 (5) Z ext (ω) = Z (NxN) (6) where n and m are the numbers of metallic layers in SC and communication cables (optical fiber OF cables) respectively, (in this case n = 6, m = 3). The indexes j, k in (4) represents the number of conductor in SC cables where as the indexes p, q represent the number of communication cables. Z isc(nxn) and Z if O(mxm) are the internal impedance matrices of tubular conductors and can be obtained using the exact [2] or the approximate formulations [1]. There are as many columns of zeroes in Z int (ω) and in Z p (ω) as the number of metallic layers in the surrounding pipe. In (6) N stands for the number of metallic elements in the umbilical and all elements are equal to a value Z (sea return impedance) which is obtained assuming an unbounded, homogeneous, media in which the internal media (sea) is given by the outermost umbilical radius and an infinite external radius. The expression for Z is given by [4], [5] Z = ρ η w K (η w R) 2πR K 1 (η w R) As the umbilical cable (UC) has a second metallic layer the expression in (5) the elements are slightly different from the classical approach propose in [3] and are given by (7) TABLE I Evaluated formulae Submarine Cable Method Internal Pipe Sea impedance impedance impedance SASB Schelkunoff Ametani + Schelkunoff Bianchi Wedepohl Ametani + Wedepohl Bianchi Z c1 = z p1e 2z p1m + z p1is + z p2i +z p2e 2z p2m + z p2is Z c2 = z p1e z p1m + z p1is + z p2i +z p2e z p2m + z p2is Z c3 = z p1e + z p1is + z p2i + z p2e 2z p2m + z p2is Z c4 = z p2e z p2m + z p2is (8) A. Unconventional Submarine Cables Applying the methodology proposed in [3] to the umbilical cable system shown in Fig. 1, the impedance matrices per unit length in (2) are given by: Z int (ω) = Z isc(nxn) Z if O(mxm) (3) Z psc(jxk) Z psc,f O Z p (ω) = Z pf O,SC Z pf O(pxq) (4) Z c5 = z p2e + z p2is where z pi, z pe and z pm are the internal, external and mutual pipe impedances. The pipe impedances are basically the same as the internal surface sheath impedance, the mutual impedance between layers and the external surface sheath impedance given by [1], [2], [5]. The approximate expressions given in [1] present suitable accuracy just when the condition (r e r i )/(r e + r i ) < 1/8 is respected, where r e and r i are the external and internal radius of a tubular conductor. III. Modal Propagation Funtions For the analysis of propagation characteristics, the umbilical cable shown in Fig. 1 was analyzed from 1 Hz

3 Attenuation (db/km) 3 to 1 MHz. The propagation constants are obtained from the square root of eigenvalues of the Z(ω)Y (ω). To avoid artificial eigenvalue/eigenvector switch-over a switch back procedure was used [8]. The modal propagation velocities are shown in Fig. 2 while the modal damping is depicted in Fig. 3. Modal velocity (km/ms) Fig. 2. Fig MODE 9 MODES 1,11 MODE 8 MODE Modal propagation velocity MODE 9 MODE 8 MODES 1,11 Frequency (Hz) MODES 6, 7 Frequency (Hz) MODES 6, 7 MODE 1 MODES 3, 4 MODE 2 MODE 5 MODE 1 MODES 3, 4 MODE Modal damping As the umbilical cable has a peculiar structure it is interesting to evaluate how the modal currents are distributed in such cable. This can be done by an analysis of the current transformation matrix, T i, relating modal and actual currents. Unfortunately, the modal transformation matrix has a strong frequency dependence. The common procedure is such cases it to approximate as the following T iapp = R[Ti ] ω Ω (9) where Ω is the high (or highest) angular frequency value. As suggested in [6] a value of Ω = 2π1 6 was adopted. Therefore, using T iapp calculated at 1 MHz, the modes present the following characteristics: mode 1 is an inter-sheath mode, it propagates in the inner metallic layer of the first pipe and returns in the sheathes of SC and communication cables. It is a slow mode and has the higher damping due to the magnetic permeability of the pipe type; mode 2 is sea return mode, the current propagates through the outermost metallic layer of the umbilical and returns through the sea. It has also a high damping and lowest propagation speed due to the high capacitance of the cable and the high inductance of the external path; modes 3 and 4 are also inter-sheath modes that relates SC and OF cables. These two modes present basically the same characteristics beacuse the SC and OF cables are symmetrically distributed inside the pipe; in mode 5 the current propagates through the sheathes of SC cables and return through the sheathes of the nearest OF cable with a small fraction of the current returning through the pipe. Although it has the same behavior as modes 3 and 4, this mode presents a higher speed and smaller damping; modes 6 and 7 are similar to modes 3 and 4 although they possess a smaller speed and a higher damping; mode 8 is a inter-pipe mode where the current propagates through the internal metallic layer and return through the external layer of the pipe modes 9, 1 and 11 are purely coaxial ones as the current propagates in one core and return in the sheath of the same or the nearest SC cable. As the SC cable are symmetric inside the pipe the three modes present the same behavior, these modes have the higher propagation velocities and smaller damping. IV. Time-domain Analysis For the time domain three configurations were considered. The umbilical cable was modeled in the frequency domain and a Numerical Laplace Transform was used to obtain the time-domain responses. The numerical Laplace Transform used in this work is summarized in Appendix B while the data for the umbilical cable are shown in Appendix A. In all test cases, the system was simulated using SASB ( exact impedance formulation) and (approximate impedance formulation). The first test is shown in Fig. 4 where the input is a 6 Hz, symmetric, balanced three-phase sinusoidal voltage and the other conductors are grounded on the source side. The sheathes voltages at the receiving end of the umbilical cable obtained using SASB and formulation are shown in Fig. 5. The agreement between the two formulation is very good. The highest value of the mismatch found in this case is of.9 pu. AC 3φ Fig. 4. Test Case # 1 three phase single core cables sheathes communication cables first armor second armor v 1abc

4 4.4 PhaseA PhaseB PhaseC.8 PhaseA PhaseB PhaseC Fig. 5. Sheath voltages for the first test Fig. 8. Sheath voltages test case # 3 The second test case is similar to the first one, but now there are no grounded conductors. The sheathes voltages at the receiving end are shown in Fig. 6. Again there is a good match between SASB and formulations. The highest mismatch found for this case was of.1 pu. case, the mismatch between simulated results was very small, the highest value was below.1 pu..6.5 Pipe 1 Pipe PhaseA PhaseB PhaseC Fig Sheath voltages for the second test Fig. 7. Test case # 3 The third test is a step voltage applied to one of the core conductors while the other terminals remain open as shown in Fig. 7. In this case is interesting to analyze the voltages induced on the pipes due to a sudden change in the system input voltage. Fig. 8 presents the sheath voltages and Fig. 9 depicts the pipe voltage. Again in this Fig. 9. Pipe voltages test case # 3 V. Conclusions This paper has presented analyzes of propagation characteristics and a time domain transient response of an unconventional cable system used in the oil industry. Unlike, underground cable systems, an umbilical cable system has not be implemented directly in EMT type programs. So a stand alone CC routine was created in order to analyze the overall performance of the system. This paper has also investigated whether the approximate formulae commonly used in underground cable system is suitable for the analysis of such a cable. The results indicate that it is possible to use these approximated expressions as long as they are used only for tubular conductors. Nevertheless, a check of validity is also implemented. In other words, the use of approximate formula implies that one check whether the condition of validity of the expressions is possible. The use of approximate expression is particularly useful for frequency domain analyzes where one may need several frequency samples. For instance, using the approximate expressions for the time-domain analysis the total simulation time was 28.7% of the total time to evaluate the system using the exact expressions. In the case of modal

5 5 propagation analysis as less frequency samples are involved the total time to express the expression using approximate formulae was 45.95% of the time needed to run the exact expressions. Appendix A Cable Data The cable presented in the Fig. 1 is an umbilical cable composed of three SC power cable system, a communication system and two metallic layers. The space between the two metallic layers is filled with two layers of EPR. Inside this dielectric filling there are also non-metallic hydraulic hoses. Power cable - r c = m, r i1 = m, r s = m, r i2 = m, ρ c = ρ s = Ω.m, ɛ r1 = 3. e ɛ r2 = Signal cable - r ai = m, r ae = m, r e = m, ρ a = Ω.m e η 3 = 2.3. First Pipe Type - r p1 = m, r p2 = m, r p3 = m, ρ a = Ω.m, µ p1 = 2, η p1 = 3. e η p2 = 2.3(HDPE - High density polyethylene). Inter-pipes - r p4 = m e η p4 = 2.3. Second Pipe Type - r p5 = m, r p6 = m, r p3 = m, ρ p2 = Ω.m, µ p2 = 4 e η p3 = 2.3(HDPE). Transmission system - length = m, ρ w =.2 Ω.m(HDPE). Appendix B Numerical Laplace Transform There are several possibilities to obtain the inverse transform of a frequency domain data. Firstly, the system was modeled in the frequency domain using real frequencies and the inverse transform was approximated by an infinite series. However, this procedure was very timeconsuming and the series had a slow convergence rate thus a large number of frequency samples were needed. Wilcox in [9] presented an elegant and efficient procedure to obtain the time-domain responses. It uses a complex frequency s = α + jω so the samples are calculated in an axis parallel to the imaginary one, i.e. instead of a real angular frequency ω a complex one given by ω jα, α > is used. Thus if G(s) is the response of a particular system in the complex frequency domain s, its time-domain counterpart g(t) is given by g(t) = exp(αt) F 1 (G(s)) (1) t If G(s) has uniformly spaced samples with respect to the angular frequency ω it is possible to replace F 1 (G(s)) IFFT(G(s)) where IFFT indicates the Inverse Fast Fourier Transform. The observation time considered was 15 ms and 496 frequency samples were used. To minimize Gibbs effects a Hanning Windows was considered, the damping coefficient was chosen based on the procedure used in [1], [11]. References [1] L. M. Wedepohl and D. J. Wilcox, Transient analysis of underground power-transmission system - system model and wave propagation characteristics, Proceedings of IEE, vol. 12, no. 2, pp , [2] S. A. Schelkunoff, The electromagnetic theory of coaxial transmission line and cylindrical shields, Bell Syst. Tech J., vol. 13, pp , [3] A. Ametani, A general formulation of impedance and admittance of cables, IEEE Trans. on PAS, vol. PAS-99, pp , May 198. [4] G. Bianchi and G. Luoni, Induced currents and losses in singlecore submarine cables, IEEE Trans. on Power App. and Syst., vol. Vol. PAS-95 nâř1, pp , [5] H. Dommel, EMTP Theory Book. MicroTran Power System Analysis Corporation, [6] B. Gustavsen, A Study of overvoltages in high voltage cables with emphasis on sheath overvoltages. PhD thesis, NTH, Institutt for Elkraftteknikk Trondheim, [7] A. Ametani, The application of the fast fourier transform to electrical transients phenomena, Int. Journal of Electrical Engineering Education, vol. 1, no. 4, pp , [8] L. M. Wedepohl, H. V. Nguyen, G. W. Irwin, Frequency- Dependent Transformation Matrices for Untransposed Transmission Line using a Newton-Raphson Method, IEEE Transactions on Power Systems, vol. 11, no. 3, pp , 1996 [9] D. J.Wilcox, Numerical Laplace Transformation and Inversion, International Journal Elect. Eng. vol. 15, pp , [1] F. A. Uribe, J. L. Naredo, P. Moreno, L. Guardado, Electromagnetic Transients in underground transmission systems through the numerical Laplace Transform, International Journal of Electrical Power and Energy Systems, 22, 24, [11] A. Ramirez, P. Gomez, P. Moreno, A. Gutierrez Frequency Domain Analysis of Electromagnetic Transients through the Numerical Laplace Transform, IEEE Power Engineering Society General Meeting, 24 Paulo E.D. Rocha was born in Rio de Janeiro, Brazil, in He received the degree of Electrical Engineer in 24 from the CEFET- RJ, he is currently working toward the M.Sc degree in Federal University of Rio de Janeiro. His main interests include simulation of electromagnetic transients and modeling of power systems in the frequency domain. Antonio Carlos Siqueira de Lima was born in Rio de Janeiro, Brazil, in He received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the Federal University of Rio de Janeiro (UFRJ) in 1995, 1997, and 1999, respectively. Currently, he is an Associate Professor with the Electrical Engineering Department of the UFRJ where he has been since 22. In 1998, he was a Visiting Scholar with the Department of Electrical and Computer Engineering at the University of British Columbia,Vancouver, BC, Canada. From 2 to 22, he was with the Brazilian Independent System Operator, ONS, Rio de Janeiro, Brazil, dealing with electromagnetic transient studies for the Brazilian National Grid.

6 6 Sandoval Carneiro Jr. was born in Brazil in He received the degree of Electrical Engineer from the Faculty of Electrical Engineering (FEI), of the Catholic University of SÃčo Paulo, Brazil, in 1968; the M.Sc. degree from the Graduate School of Engineering (COPPE)/Federal University of Rio de Janeiro (UFRJ) in 1971 and the Ph.D. degree in Electrical Engineering from University of Nottingham, England, in From 1971 to the present date he has been a Lecturer at the Federal University of Rio de Janeiro and in 1993 was promoted to Full Professor. From 1978 to 1979 he was Deputy-Director and from 1982 to 1985 Director of COPPE/UFRJ. From 1987 to 1988 and in 1994 he has was Visiting Professor at the Department of Electrical Engineering of the University of British Columbia, Vancouver, Canada. From October 1991 to June 1992 he was General Director of CAPES - Ministry of Education Agency for Academic Furtherment. His research interests comprise Simulation of Electromagnetic Transients in Power Systems and Distribution System Analysis.